AP Calculus BC
The full AP Calculus BC curriculum: a superset of AB covering all AB topics plus advanced integration techniques, parametric and polar calculus, and infinite sequences and series.
3 units and 18 lessons, for Grade 11 to Grade 12. Free on Slate.
Unit 1: Advanced Integration Techniques
Extend the integration toolkit with three powerful methods not covered in AB.
- Integration by Parts (10 min)
- Integration by Partial Fractions (10 min)
- Improper Integrals (10 min)
Unit 2: Parametric Equations, Polar Coordinates, and Vectors
Differentiate and integrate parametric and polar curves and analyze vector-valued functions.
Unit 3: Infinite Sequences and Series
The flagship BC topic: develop rigorous convergence theory and apply Taylor series to approximate functions.
- Sequences: Convergence and Divergence (10 min)
- Introduction to Series: Geometric and Telescoping (10 min)
- The nth-Term Divergence Test and Integral Test (10 min)
- Comparison and Limit Comparison Tests (10 min)
- Alternating Series Test and Error Estimation (10 min)
- Ratio and Root Tests (10 min)
- Power Series and Radius of Convergence (10 min)
- Taylor and Maclaurin Series (10 min)
- Taylor Polynomial Error and Lagrange Remainder (10 min)
- Logistic Differential Equations (10 min)